The structures of the α-alums RbCr(SO₄)₂·12H₂O and CsCr(SeO₄)₂·12H₂O at 293 and 12 K

The crystal structures of the α-alums rubidium chromium bis(­sulfate) dodecahydrate, RbCr(SO₄)₂·12H₂O, and caesium chromium bis[tetraoxoselenate(VI)] dodecahydrate, CsCr(SeO₄)₂·12H₂O, have been determined by X-ray diffraction at 293 and 12 K. The metal atoms lie on sites and the anions lie on threefold rotation axes. The accurate and extensive data sets lead to much more precise determinations than are available from earlier work, particularly at 12 K. The changes in the atomic displacement parameters between 293 and 12 K correspond to the respective predominances of intermolecular and intramolecular vibrational effects.

S1. Comment

The alums, M^IM^III(XO₄)₂.12H₂O, like Elpasolites and Tutton salts, have played a significant role in research in physics and chemistry. In particular, the systems have been invaluable for examination of metal ions in various well defined site symmetries in native and doped single crystals.

There are many previous structural studies of alums by X-ray diffraction at room temperature. They adopt the space group Pa-3 and occur in α-, β- and γ-forms. RbCr(SO₄)₂.12H₂O has been studied only by film methods (Ledsham & Steeple, 1969) and CsCr(SeO₄)₂.12H₂O somewhat more accurately (Armstrong et al., 1990). In these two studies the X—O and M—O bond length s.u.'s vary from 0.003–0.006 Å. Lower temperatures are of considerable interest to spectroscopic studies such as those of Tregenna-Piggott & Best (1996) and Tregenna-Piggott et al. (1997), and some others we have in hand, and serve to improve the accuracy of the structural determination.

There have been a number of neutron diffraction studies of both α- and β-alums at 15 K which show no abnormal behaviour or phase change resulting from the lowering in temperature There is increased accuracy, not only in hydrogen, but also non-hydrogen, parameters compared to room temperature X-ray studies (Best & Forsyth, 1990a,b, 1991; Best et al., 1993).

We have determined by X-ray diffraction at 293 and at 12 K the crystal structures of two α-alums of interest. The results illustrate the much improved accuracy, involving a factor mostly much greater than two in s.u.'s for non-hydrogen atoms which result from the lower temperature of the measurements. The crystal geometries are all typical of alums. The angle between the Cr—O bond and the unit cell axis varies from 4.6 to 6.1°, the O11—MI—O11' angle varies from 65.7 to 66.2°, and the water molecules are twisted well out of the CrO₄ planes by an average value of 21 (3)° (Figures 1a and 1 b). These are distinct from the angles near 0°, and 60° observed for β-alums (Beattie et al., 1981).

The Cr—O bond lengths we observe apparently lengthen, due to reduced libration, from 1.960 (2) to 1.966 (1) Å as we lower the temperature from 293 to 12 K. This length agrees with that in the neutron determination of CsCr(SO₄)₂.12H₂O of 1.961 (2) (Best & Fosyth, 1990b). Of the alums measured at low temperatures, the distortions of the CrO₆ fragments from the octahedral stereochemistry that we observe in our compounds at 12 K are greater than the average observed by neutron diffraction.

The atomic displacement parameters at 12 K (Figure 1 b) show no evidence of intermolecular effects. It is well known that zero-point motion, such as we are seeing here, is dominated by intramolecular vibrational modes (Willis & Pryor, 1975). Thus, we can make the predictions which follow. (1) For Cr, S or Se, and Rb or Cs we should see relatively small (0.006–0.008 Ų) and isotropic thermal ellipsoids. (2) The O principal axes should be aligned with local bonding symmetry. (3) Terminal atoms (O1—O2) should be relatively isotropic perpendicular to the bond, and because of the relative frequencies of bond stretching and bending, motion perpendicular to the bond should exceed that parallel to it (4). The O12 displacement out of the approximate Cr—OH2 plane should be longer than the plane motion. All these predictions are borne out by experiment. Since these motions are so small this is an excellent internal test of the reliability of the measured diffraction intensities and their interpretation. We note that these requirements are more stringent than the bond rigidity tests that are commonly used at higher temperatures. The thermal motion at 293 K is greatly increased from 12 K (Figure 1a).

S2. Experimental

Single crystals of the alums were obtained by recrystallization from aqueous solution.

S3. Refinement

Room temperature and the very low temperature data sets were collected on a locally assembled Huber 512 goniometer equipped with a Displex 202D cryogenic refrigerator (Hendricksen et al., 1986; Larsen, 1995).

Selected bond lengths and angles are given in Tables 1–8. The temperature evolution of thermal motion is illustrated for the hexaaquachromium(III) and selenate molecular ions CsCr(SeO₄)₂.12H₂O in Figure 1. Lists of calculated and observed structure factors are given in the supplementary material.

The correction for the absorption by the beryllium shield was performed by PROFIT (Streltsov & Zavodnik, 1989) program.

Computing details

Data collection: local diffractometer control software for (Ia), (Ib), (IIa); Local diffractometer control software for (IIb). Cell refinement: local diffractometer control software for (Ia), (Ib), (IIa); Local diffractometer control software for (IIb). For all compounds, data reduction: PROFIT (Streltsov & Zavodnik, 1989). Program(s) used to solve structure: SHELXS97 (Sheldrick, 1990) for (Ia), (IIa), (IIb); SHELXS86 (Sheldrick, 1990) for (Ib). For all compounds, program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: SHELXTL (Sheldrick, 1983). Software used to prepare material for publication: SHELXTL for (Ia), (Ib), (IIa); SHELXTL (Sheldrick, 1983) for (IIb).

Figures

Fig. 1. Environments of the atoms in (a) RbCr(SO4)2.12H2O at 293 K and (b) CsCr(SeO4)2.12H2O at 12 K. Displacement ellipsoids are shown at the 50% probability level.

(Ia) Chromium alpha-Alums

Crystal data

RbCr(SO4)2·12H2O	Melting point: not measured K
Mr = 545.78	Mo Kα radiation, λ = 0.71073 Å
Cubic, Pa3	Cell parameters from 14 reflections
Hall symbol: -P 2ac 2ab 3	θ = 16.9–17.6°
a = 12.296 (2) Å	µ = 3.53 mm^−1
V = 1859.1 (5) Å^3	T = 293 K
Z = 4	Cube, pink
F(000) = 1108	0.46 × 0.46 × 0.44 mm
Dx = 1.950 Mg m^−3

Data collection

Huber 512 goniometer diffractometer	444 reflections with I > 2σ(I)
Radiation source: normal-focus sealed tube	Rint = 0.027
None monochromator	θmax = 25.0°, θmin = 2.9°
ω–2θ scan	h = 0→14
Absorption correction: gaussian (Xtal 3.4; Hall et al., 1994)	k = 0→14
Tmin = 0.360, Tmax = 0.420	l = −14→0
1655 measured reflections	3 standard reflections every 100 reflections
557 independent reflections	intensity decay: 0.5%

Refinement

Refinement on F^2	Secondary atom site location: difference Fourier map
Least-squares matrix: full	Hydrogen site location: inferred from neighbouring sites
R[F^2 > 2σ(F^2)] = 0.032	All H-atom parameters refined
wR(F^2) = 0.080	w = 1/[σ^2(Fo^2) + (0.0299P)^2 + 4.4211P] where P = (Fo^2 + 2Fc^2)/3
S = 1.05	(Δ/σ)max < 0.001
557 reflections	Δρmax = 0.63 e Å^−3
55 parameters	Δρmin = −0.24 e Å^−3
4 restraints	Extinction correction: SHELXL97 (Sheldrick, 1997), Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
Primary atom site location: structure-invariant direct methods	Extinction coefficient: 0.0249 (15)

Special details

Experimental. no special details

Geometry. All e.s.d.'s (except the e.s.d. in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell e.s.d.'s are taken into account individually in the estimation of e.s.d.'s in distances, angles and torsion angles; correlations between e.s.d.'s in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell e.s.d.'s is used for estimating e.s.d.'s involving l.s. planes.

Refinement. Refinement of F² against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F², conventional R-factors R are based on F, with F set to zero for negative F². The threshold expression of F² > σ(F²) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F² are statistically about twice as large as those based on F, and R- factors based on ALL data will be even larger.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq
Rb	0.0000	0.0000	0.0000	0.0453 (4)
Cr	0.5000	0.5000	0.5000	0.0177 (4)
S1	0.18670 (7)	0.18670 (7)	0.18670 (7)	0.0246 (4)
O1	0.2544 (3)	0.2544 (3)	0.2544 (3)	0.0682 (19)
O2	0.0761 (2)	0.1827 (2)	0.2308 (3)	0.0554 (9)
O11	−0.1429 (2)	0.2004 (2)	0.0477 (2)	0.0381 (7)
O12	0.34142 (19)	0.4891 (2)	0.5125 (2)	0.0280 (6)
H1	−0.173 (3)	0.212 (4)	0.1056 (19)	0.041 (13)*
H2	−0.191 (3)	0.218 (4)	0.005 (3)	0.067 (17)*
H3	0.308 (4)	0.468 (4)	0.566 (2)	0.059 (15)*
H4	0.300 (3)	0.480 (3)	0.461 (2)	0.040 (12)*

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Rb	0.0453 (4)	0.0453 (4)	0.0453 (4)	0.0107 (3)	0.0107 (3)	0.0107 (3)
Cr	0.0177 (4)	0.0177 (4)	0.0177 (4)	−0.0003 (3)	−0.0003 (3)	−0.0003 (3)
S1	0.0246 (4)	0.0246 (4)	0.0246 (4)	0.0038 (4)	0.0038 (4)	0.0038 (4)
O1	0.0682 (19)	0.0682 (19)	0.0682 (19)	−0.0160 (17)	−0.0160 (17)	−0.0160 (17)
O2	0.0444 (17)	0.0446 (17)	0.077 (2)	0.0111 (14)	0.0302 (16)	0.0234 (16)
O11	0.0334 (15)	0.0408 (16)	0.0400 (16)	−0.0049 (13)	−0.0003 (13)	0.0070 (13)
O12	0.0200 (12)	0.0379 (15)	0.0260 (14)	−0.0038 (10)	−0.0002 (10)	0.0010 (11)

Geometric parameters (Å, º)

Rb—O11^i	3.082 (3)	Cr—O12^vi	1.960 (2)
Rb—O11^ii	3.082 (3)	Cr—O12	1.960 (2)
Rb—O11^iii	3.082 (3)	Cr—O12^v	1.960 (2)
Rb—O11	3.082 (3)	Cr—O12^vii	1.960 (2)
Rb—O11^iv	3.082 (3)	Cr—O12^viii	1.960 (2)
Rb—O11^v	3.082 (3)	Cr—O12^ii	1.960 (2)
Rb—S1	3.9762 (16)	S1—O1	1.442 (6)
Rb—S1^i	3.9762 (16)	S1—O2^v	1.465 (3)
Rb—O2^v	3.739 (4)	S1—O2^ii	1.465 (3)
Rb—O2^ii	3.739 (4)	S1—O2	1.465 (3)
Rb—O2^iii	3.739 (4)	O11—H1	0.813 (10)
Rb—O2	3.739 (4)	O11—H2	0.814 (10)
Rb—O2^i	3.739 (4)	O12—H3	0.822 (10)
Rb—O2^iv	3.739 (4)	O12—H4	0.820 (10)
O11—Rb—O11^iv	65.68 (4)	O11^i—Rb—O2^iv	96.79 (7)
O11—Rb—O11^v	114.32 (4)	O11^ii—Rb—O2^iv	108.18 (7)
O11^i—Rb—O11^ii	65.68 (4)	O11^iii—Rb—O2^iv	71.82 (7)
O11^i—Rb—O11^iii	114.32 (4)	O11—Rb—O2^iv	83.21 (7)
O11^ii—Rb—O11^iii	180.00 (11)	O11^iv—Rb—O2^iv	61.17 (7)
O11^i—Rb—O11	180.00 (8)	O11^v—Rb—O2^iv	118.83 (7)
O11^ii—Rb—O11	114.32 (4)	O2^v—Rb—O2^iv	180.00 (11)
O11^iii—Rb—O11	65.68 (4)	O2^ii—Rb—O2^iv	142.79 (7)
O11^i—Rb—O11^iv	114.32 (4)	O2^iii—Rb—O2^iv	37.21 (7)
O11^ii—Rb—O11^iv	65.68 (4)	O2—Rb—O2^iv	142.79 (7)
O11^iii—Rb—O11^iv	114.32 (4)	O2^i—Rb—O2^iv	37.21 (7)
O11^i—Rb—O11^v	65.68 (4)	O11^i—Rb—S1	104.03 (5)
O11^ii—Rb—O11^v	114.32 (4)	O11^ii—Rb—S1	75.97 (5)
O11^iii—Rb—O11^v	65.68 (4)	O11^iii—Rb—S1	104.03 (5)
O11^iv—Rb—O11^v	180.0	O11—Rb—S1	75.97 (5)
O11—Rb—O2	61.17 (7)	O11^iv—Rb—S1	104.03 (5)
O11^i—Rb—O2^v	83.21 (7)	O11^v—Rb—S1	75.97 (5)
O11^ii—Rb—O2^v	71.82 (7)	O11^i—Rb—S1^i	75.97 (5)
O11^iii—Rb—O2^v	108.18 (7)	O11^ii—Rb—S1^i	104.03 (5)
O11—Rb—O2^v	96.79 (7)	O11^iii—Rb—S1^i	75.97 (5)
O11^iv—Rb—O2^v	118.83 (7)	O11—Rb—S1^i	104.03 (5)
O11^v—Rb—O2^v	61.17 (7)	O11^iv—Rb—S1^i	75.97 (5)
O11^i—Rb—O2^ii	108.18 (7)	O11^v—Rb—S1^i	104.03 (5)
O11^ii—Rb—O2^ii	61.17 (7)	S1—Rb—S1^i	180.00 (4)
O11^iii—Rb—O2^ii	118.83 (7)	O12—Cr—O12^viii	89.13 (10)
O11—Rb—O2^ii	71.82 (7)	O12—Cr—O12^v	90.87 (10)
O11^iv—Rb—O2^ii	83.21 (7)	O12^vi—Cr—O12	180.0
O11^v—Rb—O2^ii	96.79 (7)	O12^vi—Cr—O12^v	89.13 (10)
O2^v—Rb—O2^ii	37.21 (7)	O12^vi—Cr—O12^vii	90.87 (10)
O11^i—Rb—O2^iii	71.82 (7)	O12—Cr—O12^vii	89.13 (10)
O11^ii—Rb—O2^iii	118.83 (7)	O12^v—Cr—O12^vii	89.13 (10)
O11^iii—Rb—O2^iii	61.17 (7)	O12^vi—Cr—O12^viii	90.87 (10)
O11—Rb—O2^iii	108.18 (7)	O12^v—Cr—O12^viii	180.0
O11^iv—Rb—O2^iii	96.79 (7)	O12^vii—Cr—O12^viii	90.87 (10)
O11^v—Rb—O2^iii	83.21 (7)	O12^vi—Cr—O12^ii	89.13 (10)
O2^v—Rb—O2^iii	142.79 (7)	O12—Cr—O12^ii	90.87 (10)
O2^ii—Rb—O2^iii	180.00 (7)	O12^v—Cr—O12^ii	90.87 (10)
O11^i—Rb—O2	118.83 (7)	O12^vii—Cr—O12^ii	180.0
O11^ii—Rb—O2	96.79 (7)	O12^viii—Cr—O12^ii	89.13 (10)
O11^iii—Rb—O2	83.21 (7)	O1—S1—O2	109.97 (15)
O11^iv—Rb—O2	108.18 (7)	O2—S1—O2^v	108.96 (15)
O11^v—Rb—O2	71.82 (7)	O1—S1—O2^v	109.97 (15)
O2—Rb—O2^v	37.21 (7)	O1—S1—O2^ii	109.97 (15)
O2—Rb—O2^ii	37.21 (7)	O2^v—S1—O2^ii	108.96 (15)
O2^iii—Rb—O2	142.79 (7)	O2—S1—O2^ii	108.96 (15)
O11^i—Rb—O2^i	61.17 (7)	O1—S1—Rb	180.00 (15)
O11^ii—Rb—O2^i	83.21 (7)	O2^v—S1—Rb	70.03 (15)
O11^iii—Rb—O2^i	96.79 (7)	O2^ii—S1—Rb	70.03 (15)
O11—Rb—O2^i	118.83 (7)	O2—S1—Rb	70.03 (15)
O11^iv—Rb—O2^i	71.82 (7)	Rb—O11—H1	124 (3)
O11^v—Rb—O2^i	108.18 (7)	Rb—O11—H2	120 (4)
O2^v—Rb—O2^i	142.79 (7)	H1—O11—H2	101 (5)
O2^ii—Rb—O2^i	142.79 (7)	Cr—O12—H3	126 (4)
O2^iii—Rb—O2^i	37.21 (7)	Cr—O12—H4	124 (3)
O2—Rb—O2^i	180.00 (12)	H3—O12—H4	106 (5)

Symmetry codes: (i) −x, −y, −z; (ii) y, z, x; (iii) −y, −z, −x; (iv) −z, −x, −y; (v) z, x, y; (vi) −x+1, −y+1, −z+1; (vii) −y+1, −z+1, −x+1; (viii) −z+1, −x+1, −y+1.

Hydrogen-bond geometry (Å, º)

D—H···A	D—H	H···A	D···A	D—H···A
O11—H1···O1^ix	0.81 (1)	2.01 (1)	2.821 (4)	175 (4)
O11—H2···O2^x	0.81 (1)	1.96 (1)	2.763 (4)	171 (5)
O12—H3···O2^xi	0.82 (1)	1.80 (1)	2.621 (4)	178 (5)
O12—H4···O11^xii	0.82 (1)	1.80 (1)	2.620 (4)	174 (4)

Symmetry codes: (ix) x−1/2, y, −z+1/2; (x) y−1/2, −z+1/2, −x; (xi) z, −x+1/2, y+1/2; (xii) y, −z+1/2, x+1/2.

(Ib) Chromium alpha-Alums

Crystal data

RbCr(SO4)2·12H2O	Melting point: not measured K
Mr = 545.78	Mo Kα radiation, λ = 0.71073 Å
Cubic, Pa3	Cell parameters from 14 reflections
Hall symbol: -P 2ac 2ab 3	θ = 16.9–17.6°
a = 12.241 (2) Å	µ = 3.58 mm^−1
V = 1834.2 (5) Å^3	T = 12 K
Z = 4	Cube, pink
F(000) = 1108	0.46 × 0.46 × 0.44 mm
Dx = 1.976 Mg m^−3

Data collection

Huber 512 goniometer diffractometer	812 reflections with I > 2σ(I)
Radiation source: normal-focus sealed tube	Rint = 0.019
None monochromator	θmax = 30.0°, θmin = 2.9°
ω–2θ scan	h = −7→17
Absorption correction: gaussian (Xtal 3.4; Hall et al., 1994)	k = −7→17
Tmin = 0.340, Tmax = 0.403	l = −7→17
4175 measured reflections	3 standard reflections every 100 reflections
905 independent reflections	intensity decay: 0.5%

Refinement

Refinement on F^2	Secondary atom site location: difference Fourier map
Least-squares matrix: full	Hydrogen site location: inferred from neighbouring sites
R[F^2 > 2σ(F^2)] = 0.019	All H-atom parameters refined
wR(F^2) = 0.045	w = 1/[σ^2(Fo^2) + (0.0167P)^2 + 1.4261P] where P = (Fo^2 + 2Fc^2)/3
S = 1.09	(Δ/σ)max < 0.001
905 reflections	Δρmax = 0.38 e Å^−3
55 parameters	Δρmin = −0.52 e Å^−3
0 restraints	Extinction correction: SHELXL97 (Sheldrick, 1997), Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
Primary atom site location: structure-invariant direct methods	Extinction coefficient: 0.0119 (4)

Special details

Experimental. The correction for the absorption by the beryllium shield was performed by PROFIT (Streltsov & Zavodnik, 1989) program.

Geometry. All e.s.d.'s (except the e.s.d. in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell e.s.d.'s are taken into account individually in the estimation of e.s.d.'s in distances, angles and torsion angles; correlations between e.s.d.'s in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell e.s.d.'s is used for estimating e.s.d.'s involving l.s. planes.

Refinement. Refinement of F² against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F², conventional R-factors R are based on F, with F set to zero for negative F². The threshold expression of F² > σ(F²) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F² are statistically about twice as large as those based on F, and R- factors based on ALL data will be even larger.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq
Rb	0.0000	0.0000	0.0000	0.00633 (10)
Cr	0.5000	0.5000	0.5000	0.00326 (11)
S1	0.18551 (2)	0.18551 (2)	0.18551 (2)	0.00419 (12)
O1	0.25528 (7)	0.25528 (7)	0.25528 (7)	0.0089 (3)
O2	0.07270 (7)	0.18407 (8)	0.22894 (8)	0.00765 (19)
O11	−0.14175 (8)	0.19772 (8)	0.04938 (9)	0.0080 (2)
O12	0.34010 (8)	0.49132 (8)	0.51150 (8)	0.00650 (19)
H1	−0.1628 (19)	0.2029 (18)	0.109 (2)	0.029 (6)*
H2	−0.1850 (18)	0.2115 (17)	0.0076 (16)	0.018 (5)*
H3	0.312 (2)	0.4720 (19)	0.568 (2)	0.038 (7)*
H4	0.301 (2)	0.4783 (19)	0.458 (2)	0.036 (7)*

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Rb	0.00633 (10)	0.00633 (10)	0.00633 (10)	0.00195 (6)	0.00195 (6)	0.00195 (6)
Cr	0.00326 (11)	0.00326 (11)	0.00326 (11)	−0.00002 (9)	−0.00002 (9)	−0.00002 (9)
S1	0.00419 (12)	0.00419 (12)	0.00419 (12)	0.00038 (10)	0.00038 (10)	0.00038 (10)
O1	0.0089 (3)	0.0089 (3)	0.0089 (3)	−0.0021 (3)	−0.0021 (3)	−0.0021 (3)
O2	0.0052 (4)	0.0080 (4)	0.0098 (4)	0.0008 (3)	0.0034 (3)	0.0017 (3)
O11	0.0073 (4)	0.0100 (4)	0.0067 (4)	0.0003 (3)	−0.0005 (4)	0.0010 (3)
O12	0.0040 (4)	0.0095 (4)	0.0059 (4)	−0.0013 (3)	0.0000 (3)	0.0006 (3)

Geometric parameters (Å, º)

Rb—O11^i	3.039 (1)	Cr—O12^vi	1.965 (1)
Rb—O11	3.039 (1)	Cr—O12^ii	1.965 (1)
Rb—O11^ii	3.039 (1)	Cr—O12^vii	1.965 (1)
Rb—O11^iii	3.039 (1)	Cr—O12^viii	1.965 (1)
Rb—O11^iv	3.039 (1)	Cr—O12	1.965 (1)
Rb—O11^v	3.039 (1)	S1—O1	1.479 (2)
Rb—O2^v	3.704 (1)	S1—O2^v	1.4798 (9)
Rb—O2^i	3.704 (1)	S1—O2^ii	1.4798 (9)
Rb—O2^ii	3.704 (1)	S1—O2	1.4798 (9)
Rb—O2^iv	3.704 (1)	O11—H1	0.78 (3)
Rb—O2	3.704 (1)	O11—H2	0.76 (2)
Rb—O2^iii	3.704 (1)	O12—H3	0.81 (3)
Cr—O12^v	1.965 (1)	O12—H4	0.83 (3)
O11—Rb—O11^iv	65.798 (15)	O11^iv—Rb—O2	107.64 (2)
O11—Rb—O11^v	114.202 (15)	O11^v—Rb—O2	72.36 (2)
O11^i—Rb—O11	180.00 (4)	O2—Rb—O2^v	38.00 (2)
O11^i—Rb—O11^ii	65.798 (15)	O2^i—Rb—O2	180.00 (3)
O11—Rb—O11^ii	114.202 (15)	O2^ii—Rb—O2	38.00 (2)
O11^i—Rb—O11^iii	114.202 (15)	O2^iv—Rb—O2	142.00 (2)
O11—Rb—O11^iii	65.798 (15)	O11^i—Rb—O2^iii	72.36 (2)
O11^ii—Rb—O11^iii	180.00 (4)	O11—Rb—O2^iii	107.64 (2)
O11^i—Rb—O11^iv	114.202 (15)	O11^ii—Rb—O2^iii	119.85 (2)
O11^ii—Rb—O11^iv	65.798 (15)	O11^iii—Rb—O2^iii	60.15 (2)
O11^iii—Rb—O11^iv	114.202 (15)	O11^iv—Rb—O2^iii	96.87 (2)
O11^i—Rb—O11^v	65.798 (15)	O11^v—Rb—O2^iii	83.13 (2)
O11^ii—Rb—O11^v	114.203 (15)	O2^v—Rb—O2^iii	142.00 (2)
O11^iii—Rb—O11^v	65.798 (15)	O2^i—Rb—O2^iii	38.00 (2)
O11^iv—Rb—O11^v	180.0	O2^ii—Rb—O2^iii	180.00 (3)
O11—Rb—O2	60.15 (2)	O2^iv—Rb—O2^iii	38.00 (2)
O11^i—Rb—O2^v	83.13 (2)	O2—Rb—O2^iii	142.00 (2)
O11—Rb—O2^v	96.87 (2)	O12—Cr—O12^viii	88.78 (4)
O11^ii—Rb—O2^v	72.36 (2)	O12—Cr—O12^v	91.22 (4)
O11^iii—Rb—O2^v	107.64 (2)	O12^v—Cr—O12^vi	88.78 (4)
O11^iv—Rb—O2^v	119.85 (2)	O12^v—Cr—O12^ii	91.22 (4)
O11^v—Rb—O2^v	60.15 (2)	O12^vi—Cr—O12^ii	180.0
O11^i—Rb—O2^i	60.15 (2)	O12^v—Cr—O12^vii	88.78 (4)
O11—Rb—O2^i	119.85 (2)	O12^vi—Cr—O12^vii	91.22 (4)
O11^ii—Rb—O2^i	83.13 (2)	O12^ii—Cr—O12^vii	88.78 (4)
O11^iii—Rb—O2^i	96.87 (2)	O12^v—Cr—O12^viii	180.0
O11^iv—Rb—O2^i	72.36 (2)	O12^vi—Cr—O12^viii	91.22 (4)
O11^v—Rb—O2^i	107.64 (2)	O12^ii—Cr—O12^viii	88.78 (4)
O2^v—Rb—O2^i	142.00 (2)	O12^vii—Cr—O12^viii	91.22 (4)
O11^i—Rb—O2^ii	107.64 (2)	O12^vi—Cr—O12	88.78 (4)
O11—Rb—O2^ii	72.36 (2)	O12^ii—Cr—O12	91.22 (4)
O11^ii—Rb—O2^ii	60.15 (2)	O12^vii—Cr—O12	180.0
O11^iii—Rb—O2^ii	119.85 (2)	O1—S1—O2	109.77 (4)
O11^iv—Rb—O2^ii	83.13 (2)	O1—S1—O2^v	109.77 (4)
O11^v—Rb—O2^ii	96.87 (2)	O1—S1—O2^ii	109.77 (4)
O2^v—Rb—O2^ii	38.00 (2)	O2^v—S1—O2^ii	109.17 (4)
O2^i—Rb—O2^ii	142.00 (2)	O2^v—S1—O2	109.17 (4)
O11^i—Rb—O2^iv	96.87 (2)	O2^ii—S1—O2	109.17 (4)
O11—Rb—O2^iv	83.13 (2)	O1—S1—Rb	180.00 (5)
O11^ii—Rb—O2^iv	107.64 (2)	O2^v—S1—Rb	70.23 (4)
O11^iii—Rb—O2^iv	72.36 (2)	O2^ii—S1—Rb	70.23 (4)
O11^iv—Rb—O2^iv	60.15 (2)	O2—S1—Rb	70.23 (4)
O11^v—Rb—O2^iv	119.85 (2)	S1—O2—Rb	87.69 (4)
O2^v—Rb—O2^iv	180.00 (2)	Rb—O11—H1	116.2 (17)
O2^i—Rb—O2^iv	38.00 (2)	Rb—O11—H2	116.3 (16)
O2^ii—Rb—O2^iv	142.00 (2)	H1—O11—H2	113 (2)
O11^i—Rb—O2	119.85 (2)	Cr—O12—H3	119.7 (17)
O11^ii—Rb—O2	96.87 (2)	Cr—O12—H4	122.3 (17)
O11^iii—Rb—O2	83.13 (2)	H3—O12—H4	112 (2)

Symmetry codes: (i) −x, −y, −z; (ii) y, z, x; (iii) −y, −z, −x; (iv) −z, −x, −y; (v) z, x, y; (vi) −y+1, −z+1, −x+1; (vii) −x+1, −y+1, −z+1; (viii) −z+1, −x+1, −y+1.

Hydrogen-bond geometry (Å, º)

D—H···A	D—H	H···A	D···A	D—H···A
O11—H1···O1^ix	0.78 (3)	2.04 (3)	2.7933 (15)	162 (2)
O11—H2···O2^x	0.76 (2)	2.02 (2)	2.7541 (15)	166 (2)
O12—H3···O2^xi	0.81 (3)	1.83 (3)	2.6321 (14)	171 (2)
O12—H4···O11^xii	0.83 (3)	1.79 (3)	2.6087 (14)	171 (3)

Symmetry codes: (ix) x−1/2, y, −z+1/2; (x) y−1/2, −z+1/2, −x; (xi) z, −x+1/2, y+1/2; (xii) y, −z+1/2, x+1/2.

(IIa) Chromium alpha-Alums

Crystal data

CsCr(SeO4)2·12H2O	Melting point: not measured K
Mr = 687.02	Mo Kα radiation, λ = 0.71073 Å
Cubic, Pa3	Cell parameters from 14 reflections
Hall symbol: -P 2ac 2ab 3	θ = 16.4–17.1°
a = 12.585 (1) Å	µ = 6.11 mm^−1
V = 1993.2 (3) Å^3	T = 293 K
Z = 4	Prism, dark violet
F(000) = 1324	0.65 × 0.64 × 0.63 mm
Dx = 2.289 Mg m^−3

Data collection

Huber 512 goniometer diffractometer	549 reflections with I > 2σ(I)
Radiation source: normal-focus sealed tube	Rint = 0.020
None monochromator	θmax = 25.0°, θmin = 2.8°
ω–2θ scan	h = 0→14
Absorption correction: gaussian (Xtal 3.4; Hall et al., 1994)	k = 0→14
Tmin = 0.138, Tmax = 0.189	l = −14→0
1751 measured reflections	3 standard reflections every 100 reflections
589 independent reflections	intensity decay: 0.5%

Refinement

Refinement on F^2	Secondary atom site location: difference Fourier map
Least-squares matrix: full	Hydrogen site location: inferred from neighbouring sites
R[F^2 > 2σ(F^2)] = 0.020	All H-atom parameters refined
wR(F^2) = 0.044	w = 1/[σ^2(Fo^2) + (0.0194P)^2 + 0.7907P] where P = (Fo^2 + 2Fc^2)/3
S = 1.26	(Δ/σ)max < 0.001
589 reflections	Δρmax = 0.26 e Å^−3
55 parameters	Δρmin = −0.54 e Å^−3
4 restraints	Extinction correction: SHELXL97 (Sheldrick, 1997), Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
Primary atom site location: structure-invariant direct methods	Extinction coefficient: 0.0166 (6)

Special details

Experimental. no special details

Geometry. All e.s.d.'s (except the e.s.d. in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell e.s.d.'s are taken into account individually in the estimation of e.s.d.'s in distances, angles and torsion angles; correlations between e.s.d.'s in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell e.s.d.'s is used for estimating e.s.d.'s involving l.s. planes.

Refinement. Refinement of F² against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F², conventional R-factors R are based on F, with F set to zero for negative F². The threshold expression of F² > σ(F²) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F² are statistically about twice as large as those based on F, and R- factors based on ALL data will be even larger.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq
Cs	0.0000	0.0000	0.0000	0.03787 (19)
Cr	0.5000	0.5000	0.5000	0.0181 (2)
Se	0.184457 (19)	0.184457 (19)	0.184457 (19)	0.02265 (18)
O1	0.25909 (17)	0.25909 (17)	0.25909 (17)	0.0503 (11)
O2	0.06434 (16)	0.17811 (15)	0.23339 (17)	0.0416 (5)
O11	−0.14271 (16)	0.20834 (16)	0.04678 (18)	0.0367 (5)
O12	0.34454 (15)	0.49205 (15)	0.50984 (14)	0.0271 (4)
H1	−0.167 (3)	0.213 (3)	0.1063 (15)	0.062 (12)*
H2	−0.194 (2)	0.218 (4)	0.009 (3)	0.072 (14)*
H3	0.314 (2)	0.474 (3)	0.5640 (16)	0.049 (10)*
H4	0.305 (2)	0.475 (3)	0.461 (2)	0.059 (12)*

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Cs	0.03787 (19)	0.03787 (19)	0.03787 (19)	0.00343 (11)	0.00343 (11)	0.00343 (11)
Cr	0.0181 (2)	0.0181 (2)	0.0181 (2)	−0.00016 (19)	−0.00016 (19)	−0.00016 (19)
Se	0.02265 (18)	0.02265 (18)	0.02265 (18)	0.00290 (9)	0.00290 (9)	0.00290 (9)
O1	0.0503 (11)	0.0503 (11)	0.0503 (11)	−0.0106 (10)	−0.0106 (10)	−0.0106 (10)
O2	0.0329 (11)	0.0363 (11)	0.0555 (12)	0.0057 (8)	0.0217 (10)	0.0145 (9)
O11	0.0311 (10)	0.0406 (11)	0.0385 (12)	−0.0043 (9)	−0.0003 (10)	0.0069 (10)
O12	0.0195 (9)	0.0380 (11)	0.0237 (10)	−0.0034 (7)	0.0015 (7)	0.0004 (8)

Geometric parameters (Å, º)

Cs—O11^i	3.232 (2)	Cr—O12^v	1.963 (2)
Cs—O11^ii	3.232 (2)	Cr—O12^iii	1.963 (2)
Cs—O11^iii	3.232 (2)	Cr—O12^vii	1.963 (2)
Cs—O11	3.232 (2)	Cr—O12	1.963 (2)
Cs—O11^iv	3.232 (2)	Cr—O12^viii	1.963 (2)
Cs—O11^v	3.232 (2)	Se—O1	1.627 (4)
Cs—O2^ii	3.782 (2)	Se—O2	1.634 (2)
Cs—O2	3.782 (2)	Se—O2^v	1.634 (2)
Cs—O2^v	3.782 (2)	Se—O2^iii	1.634 (2)
Cs—O2^iv	3.782 (2)	O11—H1	0.81 (1)
Cs—O2^iii	3.782 (2)	O11—H2	0.82 (1)
Cs—O2^i	3.782 (2)	O12—H3	0.82 (1)
Cr—O12^vi	1.963 (2)	O12—H4	0.82 (1)
O11—Cs—O11^ii	66.16 (3)	O11^iv—Cs—O2^i	70.15 (5)
O11—Cs—O11^iii	113.84 (3)	O11^v—Cs—O2^i	120.21 (5)
O11^i—Cs—O11^ii	113.84 (3)	O2—Cs—O2^iii	41.13 (5)
O11^i—Cs—O11^iii	66.16 (3)	O2^ii—Cs—O2^iv	41.13 (5)
O11^ii—Cs—O11^iii	180.00 (6)	O2—Cs—O2^iv	180.00 (4)
O11^i—Cs—O11	66.16 (3)	O2^v—Cs—O2^iv	138.87 (5)
O11^i—Cs—O11^iv	113.84 (3)	O2^v—Cs—O2^iii	41.13 (5)
O11^ii—Cs—O11^iv	113.84 (3)	O2^iv—Cs—O2^iii	138.87 (5)
O11^iii—Cs—O11^iv	66.16 (3)	O2^ii—Cs—O2^i	41.13 (5)
O11—Cs—O11^iv	180.0	O2—Cs—O2^i	138.87 (5)
O11^i—Cs—O11^v	180.00 (8)	O2^v—Cs—O2^i	180.0
O11^ii—Cs—O11^v	66.16 (3)	O2^iv—Cs—O2^i	41.13 (5)
O11^iii—Cs—O11^v	113.84 (3)	O2^iii—Cs—O2^i	138.87 (5)
O11—Cs—O11^v	113.84 (3)	O2^ii—Cs—O2^iii	180.00 (5)
O11^iv—Cs—O11^v	66.16 (3)	O2^ii—Cs—O2^v	138.87 (5)
O11—Cs—O2	59.79 (5)	O2—Cs—O2^v	41.13 (5)
O11^i—Cs—O2^ii	70.15 (5)	O2^ii—Cs—O2	138.87 (5)
O11^ii—Cs—O2^ii	59.79 (5)	O12—Cr—O12^vi	89.13 (8)
O11^iii—Cs—O2^ii	120.21 (5)	O12—Cr—O12^iii	90.87 (8)
O11—Cs—O2^ii	81.38 (5)	O12^vi—Cr—O12^v	89.13 (8)
O11^iv—Cs—O2^ii	98.62 (5)	O12^vi—Cr—O12^iii	180.0
O11^v—Cs—O2^ii	109.85 (5)	O12^v—Cr—O12^iii	90.87 (8)
O11^i—Cs—O2	81.38 (5)	O12^vi—Cr—O12^vii	90.87 (8)
O11^ii—Cs—O2	109.85 (5)	O12^v—Cr—O12^vii	180.0
O11^iii—Cs—O2	70.15 (5)	O12^iii—Cr—O12^vii	89.13 (8)
O11^iv—Cs—O2	120.21 (5)	O12^v—Cr—O12	90.87 (8)
O11^v—Cs—O2	98.62 (5)	O12^vii—Cr—O12	89.13 (8)
O11^i—Cs—O2^v	120.21 (5)	O12^vi—Cr—O12^viii	90.87 (8)
O11^ii—Cs—O2^v	81.38 (5)	O12^v—Cr—O12^viii	89.13 (8)
O11^iii—Cs—O2^v	98.62 (5)	O12^iii—Cr—O12^viii	89.13 (8)
O11—Cs—O2^v	70.15 (5)	O12^vii—Cr—O12^viii	90.87 (8)
O11^iv—Cs—O2^v	109.85 (5)	O12—Cr—O12^viii	180.00 (11)
O11^v—Cs—O2^v	59.79 (5)	O1—Se—O2	110.16 (8)
O11^i—Cs—O2^iv	98.62 (5)	O2—Se—O2^iii	108.77 (8)
O11^ii—Cs—O2^iv	70.15 (5)	O1—Se—O2^v	110.16 (8)
O11^iii—Cs—O2^iv	109.85 (5)	O2—Se—O2^v	108.77 (8)
O11—Cs—O2^iv	120.21 (5)	O1—Se—O2^iii	110.16 (8)
O11^iv—Cs—O2^iv	59.79 (5)	O2^v—Se—O2^iii	108.77 (8)
O11^v—Cs—O2^iv	81.38 (5)	O1—Se—Cs	180.00 (6)
O11^i—Cs—O2^iii	109.85 (5)	O2—Se—Cs	69.84 (8)
O11^ii—Cs—O2^iii	120.21 (5)	O2^v—Se—Cs	69.84 (8)
O11^iii—Cs—O2^iii	59.79 (5)	O2^iii—Se—Cs	69.84 (8)
O11—Cs—O2^iii	98.62 (5)	Se—O2—Cs	86.24 (8)
O11^iv—Cs—O2^iii	81.38 (5)	Cs—O11—H1	116 (3)
O11^v—Cs—O2^iii	70.15 (5)	Cs—O11—H2	117 (3)
O11^i—Cs—O2^i	59.79 (5)	H1—O11—H2	104 (4)
O11^ii—Cs—O2^i	98.62 (5)	Cr—O12—H3	123 (2)
O11^iii—Cs—O2^i	81.38 (5)	Cr—O12—H4	125 (3)
O11—Cs—O2^i	109.85 (5)	H3—O12—H4	105 (3)

Symmetry codes: (i) −y, −z, −x; (ii) −z, −x, −y; (iii) z, x, y; (iv) −x, −y, −z; (v) y, z, x; (vi) −z+1, −x+1, −y+1; (vii) −y+1, −z+1, −x+1; (viii) −x+1, −y+1, −z+1.

Hydrogen-bond geometry (Å, º)

D—H···A	D—H	H···A	D···A	D—H···A
O11—H1···O1^ix	0.81 (1)	2.02 (1)	2.811 (3)	166 (4)
O11—H2···O2^x	0.82 (1)	1.95 (1)	2.753 (3)	169 (4)
O12—H3···O2^xi	0.82 (1)	1.82 (1)	2.635 (3)	175 (3)
O12—H4···O11^xii	0.82 (1)	1.80 (1)	2.620 (3)	173 (4)

Symmetry codes: (ix) x−1/2, y, −z+1/2; (x) y−1/2, −z+1/2, −x; (xi) z, −x+1/2, y+1/2; (xii) y, −z+1/2, x+1/2.

(IIb) Chromium alpha-Alums

Crystal data

CsCr(SeO4)2·12H2O	Melting point: not measured K
Mr = 687.02	Mo Kα radiation, λ = 0.71073 Å
Cubic, Pa3	Cell parameters from 14 reflections
Hall symbol: -P 2ac 2ab 3	θ = 16.5–17.2°
a = 12.522 (3) Å	µ = 6.20 mm^−1
V = 1963.5 (8) Å^3	T = 12 K
Z = 4	Prism, dark violet
F(000) = 1324	0.65 × 0.64 × 0.63 mm
Dx = 2.324 Mg m^−3

Data collection

Huber 512 goniometer diffractometer	916 reflections with I > 2σ(I)
Radiation source: normal-focus sealed tube	Rint = 0.033
None monochromator	θmax = 30.0°, θmin = 2.8°
ω–2θ scan	h = −7→17
Absorption correction: gaussian Xtal 3.4 (Hall, King & Stewart, 1994)	k = −7→17
Tmin = 0.132, Tmax = 0.188	l = −7→17
4443 measured reflections	3 standard reflections every 100 reflections
963 independent reflections	intensity decay: 0.5%

Refinement

Refinement on F^2	Secondary atom site location: difference Fourier map
Least-squares matrix: full	Hydrogen site location: inferred from neighbouring sites
R[F^2 > 2σ(F^2)] = 0.019	H atoms treated by a mixture of independent and constrained refinement
wR(F^2) = 0.042	w = 1/[σ^2(Fo^2) + (0.0122P)^2 + 2.1334P] where P = (Fo^2 + 2Fc^2)/3
S = 1.31	(Δ/σ)max = 0.001
963 reflections	Δρmax = 0.46 e Å^−3
55 parameters	Δρmin = −0.45 e Å^−3
4 restraints	Extinction correction: SHELXL, Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
Primary atom site location: structure-invariant direct methods	Extinction coefficient: 0.0092 (3)

Special details

Experimental. The correction for the absorption by the beryllium shield was performed by PROFIT (Streltsov & Zavodnik, 1989) program.

Geometry. All e.s.d.'s (except the e.s.d. in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell e.s.d.'s are taken into account individually in the estimation of e.s.d.'s in distances, angles and torsion angles; correlations between e.s.d.'s in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell e.s.d.'s is used for estimating e.s.d.'s involving l.s. planes.

Refinement. Refinement of F² against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F², conventional R-factors R are based on F, with F set to zero for negative F². The threshold expression of F² > σ(F²) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F² are statistically about twice as large as those based on F, and R- factors based on ALL data will be even larger.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq
Cs	0.0000	0.0000	0.0000	0.00401 (8)
Cr	0.5000	0.5000	0.5000	0.00283 (13)
Se	0.182558 (13)	0.182558 (13)	0.182558 (13)	0.00297 (9)
O1	0.25820 (10)	0.25820 (10)	0.25820 (10)	0.0077 (4)
O2	0.06066 (10)	0.17818 (11)	0.23076 (10)	0.0066 (2)
O11	−0.14282 (11)	0.20648 (11)	0.04845 (11)	0.0074 (2)
O12	0.34334 (11)	0.49408 (11)	0.50842 (11)	0.0060 (2)
H1	−0.164 (3)	0.208 (4)	0.1128 (14)	0.069 (15)*
H2	−0.1937 (18)	0.221 (3)	0.007 (2)	0.024 (8)*
H3	0.313 (2)	0.478 (3)	0.5664 (15)	0.033 (9)*
H4	0.299 (2)	0.483 (3)	0.458 (2)	0.033 (9)*

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Cs	0.00401 (8)	0.00401 (8)	0.00401 (8)	0.00036 (5)	0.00036 (5)	0.00036 (5)
Cr	0.00283 (13)	0.00283 (13)	0.00283 (13)	−0.00016 (13)	−0.00016 (13)	−0.00016 (13)
Se	0.00297 (9)	0.00297 (9)	0.00297 (9)	0.00020 (6)	0.00020 (6)	0.00020 (6)
O1	0.0077 (4)	0.0077 (4)	0.0077 (4)	−0.0016 (4)	−0.0016 (4)	−0.0016 (4)
O2	0.0042 (5)	0.0070 (5)	0.0087 (6)	0.0007 (5)	0.0034 (5)	0.0015 (5)
O11	0.0060 (5)	0.0090 (6)	0.0073 (6)	−0.0001 (5)	−0.0002 (5)	0.0010 (5)
O12	0.0041 (6)	0.0089 (6)	0.0049 (6)	−0.0009 (4)	−0.0002 (4)	0.0002 (5)

Geometric parameters (Å, º)

Cs—O11^i	3.202 (2)	Cr—O12^ii	1.966 (1)
Cs—O11^ii	3.202 (2)	Cr—O12^vi	1.966 (1)
Cs—O11^iii	3.202 (2)	Cr—O12^vii	1.966 (1)
Cs—O11	3.202 (2)	Cr—O12^viii	1.966 (1)
Cs—O11^iv	3.202 (2)	Cr—O12^i	1.966 (1)
Cs—O11^v	3.202 (2)	Se—O1	1.641 (2)
Cs—O2^iii	3.729 (2)	Se—O2	1.642 (1)
Cs—O2^iv	3.729 (2)	Se—O2^i	1.642 (1)
Cs—O2^v	3.729 (2)	Se—O2^ii	1.642 (1)
Cs—O2	3.729 (2)	O11—H1	0.849 (10)
Cs—O2^i	3.729 (2)	O11—H2	0.844 (10)
Cs—O2^ii	3.729 (2)	O12—H3	0.844 (10)
Cr—O12	1.966 (1)	O12—H4	0.849 (10)
O11—Cs—O11^iv	66.18 (2)	O11^iv—Cs—O2^ii	121.08 (3)
O11—Cs—O11^ii	113.82 (2)	O11^v—Cs—O2^ii	81.08 (3)
O11^i—Cs—O11^ii	113.82 (2)	O2—Cs—O2^ii	41.98 (3)
O11^i—Cs—O11^iii	180.00 (5)	O2^iii—Cs—O2^v	41.98 (3)
O11^ii—Cs—O11^iii	66.18 (2)	O2^iv—Cs—O2^v	41.98 (3)
O11^i—Cs—O11	113.82 (2)	O2^i—Cs—O2^ii	41.98 (3)
O11^iii—Cs—O11	66.18 (2)	O2^iii—Cs—O2^iv	41.98 (3)
O11^i—Cs—O11^iv	66.18 (2)	O2^iii—Cs—O2^ii	138.02 (3)
O11^ii—Cs—O11^iv	180.00 (4)	O2^iv—Cs—O2^ii	180.00 (4)
O11^iii—Cs—O11^iv	113.82 (2)	O2^v—Cs—O2^ii	138.02 (3)
O11^i—Cs—O11^v	66.18 (2)	O2^iii—Cs—O2^i	180.00 (3)
O11^ii—Cs—O11^v	66.18 (2)	O2^iv—Cs—O2^i	138.02 (3)
O11^iii—Cs—O11^v	113.82 (2)	O2^v—Cs—O2^i	138.02 (3)
O11—Cs—O11^v	180.00 (4)	O2—Cs—O2^i	41.98 (3)
O11^iv—Cs—O11^v	113.82 (2)	O2^iii—Cs—O2	138.02 (3)
O11—Cs—O2	58.92 (3)	O2^iv—Cs—O2	138.02 (3)
O11^i—Cs—O2^iii	121.08 (3)	O2^v—Cs—O2	180.0
O11^ii—Cs—O2^iii	81.08 (3)	O12—Cr—O12^viii	88.97 (5)
O11^iii—Cs—O2^iii	58.92 (3)	O12—Cr—O12^ii	91.03 (5)
O11—Cs—O2^iii	109.28 (3)	O12—Cr—O12^vi	88.97 (5)
O11^iv—Cs—O2^iii	98.92 (3)	O12^ii—Cr—O12^vi	88.97 (5)
O11^v—Cs—O2^iii	70.72 (3)	O12—Cr—O12^vii	180.0
O11^i—Cs—O2^iv	109.28 (3)	O12^ii—Cr—O12^vii	88.97 (5)
O11^ii—Cs—O2^iv	121.08 (3)	O12^vi—Cr—O12^vii	91.03 (5)
O11^iii—Cs—O2^iv	70.72 (3)	O12^ii—Cr—O12^viii	180.0
O11—Cs—O2^iv	81.08 (3)	O12^vi—Cr—O12^viii	91.03 (5)
O11^iv—Cs—O2^iv	58.92 (3)	O12^vii—Cr—O12^viii	91.03 (5)
O11^v—Cs—O2^iv	98.92 (3)	O12—Cr—O12^i	91.03 (5)
O11^i—Cs—O2^v	81.08 (3)	O12^ii—Cr—O12^i	91.03 (5)
O11^ii—Cs—O2^v	109.28 (3)	O12^vi—Cr—O12^i	180.0
O11^iii—Cs—O2^v	98.92 (3)	O12^vii—Cr—O12^i	88.97 (5)
O11—Cs—O2^v	121.08 (3)	O12^viii—Cr—O12^i	88.97 (5)
O11^iv—Cs—O2^v	70.72 (3)	O1—Se—O2	110.10 (5)
O11^v—Cs—O2^v	58.92 (3)	O1—Se—O2^ii	110.10 (5)
O11^i—Cs—O2	98.92 (3)	O1—Se—O2^i	110.10 (5)
O11^ii—Cs—O2	70.72 (3)	O2—Se—O2^i	108.83 (5)
O11^iii—Cs—O2	81.08 (3)	O2—Se—O2^ii	108.83 (5)
O11^iv—Cs—O2	109.28 (3)	O2^i—Se—O2^ii	108.83 (5)
O11^v—Cs—O2	121.08 (3)	O1—Se—Cs	180.00 (4)
O11^i—Cs—O2^i	58.92 (3)	O2—Se—Cs	69.90 (5)
O11^ii—Cs—O2^i	98.92 (3)	O2^i—Se—Cs	69.90 (5)
O11^iii—Cs—O2^i	121.08 (3)	O2^ii—Se—Cs	69.90 (5)
O11—Cs—O2^i	70.72 (3)	Se—O2—Cs	85.67 (5)
O11^iv—Cs—O2^i	81.08 (3)	Cs—O11—H1	112 (3)
O11^v—Cs—O2^i	109.28 (3)	Cs—O11—H2	119 (2)
O11^i—Cs—O2^ii	70.72 (3)	H1—O11—H2	110 (4)
O11^ii—Cs—O2^ii	58.92 (3)	Cr—O12—H3	120 (2)
O11^iii—Cs—O2^ii	109.28 (3)	Cr—O12—H4	128 (2)
O11—Cs—O2^ii	98.92 (3)	H3—O12—H4	108 (3)

Symmetry codes: (i) y, z, x; (ii) z, x, y; (iii) −y, −z, −x; (iv) −z, −x, −y; (v) −x, −y, −z; (vi) −y+1, −z+1, −x+1; (vii) −x+1, −y+1, −z+1; (viii) −z+1, −x+1, −y+1.

Hydrogen-bond geometry (Å, º)

D—H···A	D—H	H···A	D···A	D—H···A
O11—H1···O1^ix	0.85 (1)	1.99 (2)	2.796 (2)	158 (4)
O11—H2···O2^x	0.84 (1)	1.91 (1)	2.740 (2)	167 (3)
O12—H3···O2^xi	0.84 (1)	1.80 (1)	2.641 (2)	171 (3)
O12—H4···O11^xii	0.85 (1)	1.76 (1)	2.609 (2)	176 (3)

Symmetry codes: (ix) x−1/2, y, −z+1/2; (x) y−1/2, −z+1/2, −x; (xi) z, −x+1/2, y+1/2; (xii) y, −z+1/2, x+1/2.